1. Field of the Invention
The invention relates to a frequency synthesiser according to the direct digital synthesis method with the capability of suppressing secondary lines in the frequency spectrum of the output frequency signal.
2. Description of the Background Art
Contemporary high-resolution broadband frequency synthesisers are essentially based upon two different methods, the fractional-N-method and the direct digital synthesis method.
In the case of the fractional-N-method, the frequency is adjusted through defined frequency division of the reference frequency in a forward branch disposed upstream of the phase-locking loop or of the output frequency of the phase-locking loop in the closed-loop branch of the phase-locking loop, in each case via one programmable frequency divider. The frequency divider operates digitally via sigma-delta modulation of a digital word acting as a reference frequency value. A high-frequency phase-locking loop can be realized through the use of high division factors in the frequency divider of the closed-loop branch. However, high division factors bring about a significant increase in the phase noise of the phase-locking loop (phase noise of the phase-locking loop=20*log (division factor of the output frequency divider)). Moreover, the sigma-delta modulator generates a quantization noise increasing further away from the carrier, which must absolutely be suppressed by the PLL. The attenuation of the increased phase noise and/or of the increasing quantization noise by means of low-pass characteristics of the phase-locking loop is purchased at the cost of poorer control dynamics of the phase-locking loop (longer transient recovery time because of reduced bandwidth of the phase-locking loop). The maximum realisable control bandwidths, according to the existing prior art are around a few KHz. The fractional-N-method also provides a comparatively poor transient recovery performance, because the algorithm of the fractional-N-method approaches the optimum in an integrating manner. A final disadvantage of the fractional-N-method is that the frequency spectrum of the output frequency contains secondary lines, which occur during the division of the output frequency signal through the fractional-N-frequency divider in the closed-loop branch of the phase-locking loop with a division factor close to a whole-number division factor (so-called “fractional-N-secondary lines”).
One advantage of the phase-locking loop is the fact that it can be realized in a comparatively cost-favorable manner and is therefore used primarily in applications in the low-price segment. The method of direct digital frequency synthesis does not suffer from the disadvantages mentioned above and is therefore used primarily in frequency synthesisers with rapid transient recovery and low-phase-noise.
A frequency synthesiser based on the method of direct digital synthesis according to document EP 0 469 233 A2 consists of a phase accumulator, which increments the phase of a phase signal cyclically at the clock pulse of a reference frequency by phase increments, which can be adjusted in a frequency word at the input of the phase accumulator. A memory unit downstream of the phase accumulator with a stored table of sine-function values supplies the sine-function values associated with the relevant phase values of the cyclical phase signal to a digital-to-analog converter at the clock pulse of the reference frequency as a time-discrete functional sequence. Smoothing through an anti-aliasing low-pass filter to the desired sinusoidal frequency signal takes place after the digital-to-analog converter.
The disadvantage with direct digital frequency synthesisers is the occurrence of secondary lines very close to the carrier in the frequency spectrum. If the lines appear close to the useful signal, these secondary lines cannot be regulated out of the frequency spectrum by a series-connected phase-locking loop with optimised bandwidth. The following reasons can be given for the occurrence of secondary lines of this kind in the frequency spectrum of the output frequency, also with reference to the specialist article: Papay, “Numerical Distortion in Single-Tone DDS”, IEEE-Instrumentation and Measurement Technology Conference, Budapest, May 21–23, 2001:                Secondary lines caused by restricted phase resolution of the phase signal in the sine table of the memory unit:        
As a result of limited memory capacity of the memory unit, all the bits of the phase signal are not used in addressing the memory cells containing the sine table. As a result of a restriction to the higher-value bits of the phase signal, the number of phase interpolation points used per sinusoidal oscillation is significantly reduced corresponding to a lower resolution of the phase interpolation points. This leads to a sawtooth phase error between the optimum phase interpolation points realisable, for example, with a 32 bit-wide phase-signal data word and the phase interpolation points actually used. This periodicity in the phase error, which corresponds to a phase modulation, leads to discrete secondary lines around the carrier frequency in the frequency spectrum of the output frequency generated.                Secondary lines caused by excessively low-amplitude resolution of the digital-to-analog converter:        
The quantization of the time-discrete sine-function values for a predetermined phase value causes an amplitude error, which is dependent upon the resolution of the quantization (number of bits for the quantization of the amplitude value). Through this quantization of the amplitude value, an amplitude error of ΔA=1/(2A*√{square root over (12)}) is caused, under the assumption that rounding errors are distributed uniformly in the range ±½ LSB (A=number of bits of the D/A converter). If the length of the phase accumulator is a whole-number multiple of the frequency word, then the phase values are repeated periodically and the quantization error associated with each phase and amplitude value provides a periodic characteristic, which leads to higher value harmonics (=secondary lines) in the frequency spectrum. In the absence of periodicity of the phase values and therefore of the amplitude values in the case of a non-whole-number ratio between frequency word and the length of the frequency accumulator, interference lines can occur throughout the frequency spectrum instead of the higher value harmonics.                Secondary lines caused by nonlinearities in the transmission characteristic of the digital-to-analog converter:        
As shown in FIG. 1, the transmission characteristic of a digital-to-analog converter generally provides a nonlinearity in the curve by comparison with an ideal-linear characteristic. This is strongly exaggerated in the presentation in FIG. 1. This may be a nonlinearity, which extends over the entire level range (a so-called integral nonlinearity) or only a deviation from the theoretical value difference for the transition between two conditions of the analog-to-digital converter (so-called differential nonlinearity). These nonlinearities are attributable to asymmetries in the internal structure of the digital-to-analog converter (e.g. asymmetries in difference amplification, power sources, resistance chains etc.). In the case of harmonic excitation, nonlinearities in the transmission behaviour lead to the generation of harmonic waves, which, once again, lead to secondary lines in the frequency spectrum of the output frequency. Because the system involved is a sampled system, aliasing can occur. As shown in FIG. 2, these aliasing effects mean that harmonic secondary lines above the first Nyquist zone can be folded into corresponding non-harmonic secondary lines within the first Nyquist zone. It is problematic that non-harmonic secondary lines of this kind in the first Nyquist zone can come to be disposed very close to the carrier frequency. While harmonic secondary lines can be removed by means of low-pass filtering, this is not a viable possibility with non-harmonic secondary lines close to the carrier.                Secondary lines caused by the non-ideal dynamic behaviour of the digital-to-analog converter:        
From a certain sampling frequency, dynamic effects become more prominent, by comparison with the static effects described in the previous paragraph, in the transmission behaviour of the digital-to-analog converter. This relates primarily to differences in rise and fall times and differences in overshooting in the case of transmission behaviour with multiple delays in the phase of sampling and holding of the time-discrete sinusoidal interpolation points (“glitches”). These dynamic interference effects are attributable to asymmetries and error adaptations in the internal structure of the digital-to-analog converter (e.g. error-adapted RC-elements, different switching times and the absence of synchronicity of individual logic units etc.). Since these dynamic interference effects occur periodically, undesired harmonics (=secondary lines), which are dominant from a given frequency by comparison with the secondary lines caused for the previously named reasons, also occur in the frequency spectrum. A minimisation of these dynamic irregularities through an additional sampling and holding while exploiting the resulting smoothing effect is not possible especially at higher sampling frequencies, because the sampling period can then become smaller than the transient recovery time.
The occurrence of secondary lines resulting from restricted phase and amplitude resolution is nowadays largely manageable. While an increased phase resolution, can be realized, for example, using advanced interpolation algorithms, an increased amplitude resolution no longer represents a substantial problem with contemporary digital-to-analog converters with 14 bit data-word width even in the upper clock-pulse frequency range of 100 MHz and above. Secondary lines caused by nonlinearities in the transmission characteristic and caused by dynamic asymmetries of the digital-to-analog converter, however, still present an unresolved problem with contemporary direct digital frequency synthesisers.